Optionally due on Saturday *or* Sunday

I have a bunch of "weekend tasks" that I want to try to get to. I want them to show up as due every Saturday. If I complete them Saturday, I want them to roll to NEXT Saturday. If I don't complete them Saturday, I want them to roll to Sunday. If I complete them Sunday, I want to see them again next Saturday. If I don't complete them Sunday, I want to see them again next Saturday.

Is this a START SATURDAY, OPTIONALLY DUE SUNDAY, complete every Sunday by DUE date situation? Or will that not do what I need?

You can't do exactly what you are describing. My suggestion is to have the weekly task due on Saturday, and if you don't do it, it will just become overdue by 1 day and you can still do it on Sunday. When you complete it (either saturday or sunday) it will move to the next saturday.